In their early history, the Jesuits were instrumental in effecting the reforms of the Council of Trent and the Counter-Reformation efforts of the Church. This did not endear them to local populations, especially in areas with large Protestant populations that were hostile towards Catholicism. They also were a key force that assisted the spread of Catholicism to the Americas when the New World was colonized. They were renowned for their obedience to the Pope and their willingness to travel anywhere in the world, sometimes under drastic conditions, to assist the spread and defense of Catholicism.
In addition to these efforts, they also are renowned for their contributions to science and education. They founded numerous institutions of higher learning and had several members of their society make important contributions to a variety of scientific fields such as physics and astronomy.
The recent history of the Jesuits has sadly, been less impressive. Although today the Jesuits still perform various missions and operate charities on behalf of the Church, modern Jesuits are mostly known for their opposition or indifference to the more contested (by secular society) areas of Church doctrine (i.e., gay marriage, women’s ordination, abortion, contraception, etc.). They were also instrumental in the development of liberation theology, a movement that was criticized in several official Church documents under Pope John Paul II by the future Pope Benedict XVI. Their most well known English language publication, America, was placed under investigation by the Vatican in the mid-2000s due to their outspoken stances against the Church and Church doctrine, mainly for their support of homosexuality, abortion, and contraception. The lead editor for the magazine was forced to resign. Many of their colleges and universities are now no more Catholic than your local community college (e.g., Georgetown University).
Today the most well-known Jesuit, at least in the western world, is probably Fr. James Martin, who is primarily known for his tacit support of homosexuality (he is also less known as a supporter of women’s ordination). Many other Jesuits, including their current Superior General, Fr. Arturo Sosa, have made headlines in recent times for their puzzling and sometimes borderline heretical comments (Fr. Sosa, in a 2017 interview questioned the authority of the Church to interpret the Scriptures when discussing the Church’s prohibition on divorce and remarriage. He also strongly implied that the devil is only symbolic, in contradiction of Church teaching in an interview later that year.). Like many of the more liberal religious orders of the Church, vocations for the Jesuits have been in a steady decline since the 1950s, and will possibly cease to exist as an order within several decades if they cannot stem the tide.